# Replace ___ by the smallest no to make it divisible by 11 9___8071

2
by akalra26

2014-10-07T17:36:39+05:30
Your answer will be 918071 - Because if the difference of the sums of the numbers in the even and odd places is 0 or divisible by 11, the whole number is divisible by 11. IN this case, 9+8+7 = 24 and 1+1 = 2 so 24 - 2 = 22, which is a multiple of 11.
2014-10-08T17:21:57+05:30

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Let us try if filling the blank by one digit solves the problem.  Let that digit be x.  If it is not possible by a single digit then we take two digits later.

9x8071 be divisible by 11.  It means the sum of odd digits and the sum of even digits differ by a multiple of 11.

So  (9+8+7) - (x+0+1) = 11 * n  for some integer n
24 - x - 1 = 11 * n
23 - x = 11 * n
the smallest value of x for which this happens is  x = 1.

so  answer is 1  and the number is  918071.